Fast ignition in (ICF) was proposed as an alternative ignition scheme aimed to reduce the drive requirements by separating fuel compression and ignition in two steps. In electron-driven fast ignition (EFI), after fuel compression stage, a fast electron jet is generated near the cone tip by an ultra-high intensity laser beam ( 10 20 W/cm 2 ). Fast electrons deposit their energy in the compressed fuel, triggering the fusion reaction. At this stage, laser pulse was entered from one direction in to the plasma region which create an anisotropy in plasma. This anisotropy is caused due to relativistic electrons flow that injected to the fuel. In presence of anisotropy, weibel Instability leading the plasma to equilibrium state and reduced free energy generated by anisotropy. This instability enhances a magnetic disturbance in the plasma. In general, non-equilibrium process is called instability case. The excited waves or disturbances in plasma produes instability. Weibel instability by strengthening the magnetic field in the perpendicular direction of the anisotropy can occurs. In this research, we have studied the instability created in the last stage of the fast ignition. For this purpose we used XOOPIC code for simulation of plasma region. This code is a tradition code in simulation of plasma regions. First we have investigated this instability in the absence of horns in the fuel ball. The results show that Weibel instability at the initial time growth and decline rapidly after reaching peak. Next we have investigated the growth of instabilities in the plasma in the presence of aluminum cone. At this case, the laser start dealing with aluminum and causes the acceleration of electrons, these electrons are entered into the plasma environment. Weibel Instability grows in the initial times less than later time. Finally, weibel Instability growt rate, after a relative reduction will rises again. Then we used a foil of gold instead of aluminum foil in the fuel zone. At this case, more energy is transferred in to the plasma. The results showed that in the case of gold, growing instability in the first times is few and at the delay time is very high. We have also calculated the exit power and compared it with results of the reference. According to the observations in the simulation, as increasing the electron flow that entered into the plasma, the plasma energy is increased. Also anisotropy and magnetic field in the initial time grow with a gentler slope and then remain constant finally. The maximum of exit power was remained more constant by increasing the leading field so that the growth rate of the weibel instability decreases at the final stage.